Modal decomposition from partial measurements

International audienceA data set over space and time is assumed to have a low rank representation in separated spatial and temporal modes. The problem of evaluating these modes from a temporal series of partial measurements is considered. Each elementary instantaneous measurement captures only a window (in space) of the observed data set, but the window position varies in time so as to cover the entire region of interest and would allow for a complete measurement would the scene be static. A novel procedure, alternative to the Gappy Proper Orthogonal Decomposition (GPOD) methodology, is introduced. It is a xed point iterative procedure where modes are evaluated sequentially. Tested upon very sparse acquisition (1% of measurements being available) and very noisy synthetic data sets (10% noise), the proposed algorithm is shown to outperform two variants of the GPOD algorithm, with much faster convergence, and better reconstruction of the entire data set

La mujer combatiente en la propaganda de los grupos insurgentes. El caso de las FARC-EP.

  Between 2004 and 2016, the Colombian guerrillas of the FARC-EP went through several mutations before signing a peace agreement that marked the end of their armed struggle. In each of these stages, what the guerrillas used to call “propaganda” has played a central role in the group’s strategy. This article analyzes 37 issues of Resistencia, the journal published clandestinely by the FARC-EP. It critically questions the evolution of female combatant representation, a central element of the FARC-EP discourse and of the propaganda war in Colombia. The article reveals two successive strategies. At first, the FARC-EP developed a discourse of symbolic compensation, offering women combatants constant tributes in their journal, but leaving little space for the actual voices of female fighters. As of 2012, the analysis reveals a process of gender mainstreaming in FARC-EP propaganda, which corresponds to the emergence of female figures in the foreground of the negotiating table in Havana. Confirming the material effects that feminist discourse can have on insurgent organizations, the analysis also reveals the persistence in Colombia of discursive strategies that seek to recycle militarized gender stereotypes produced by armed actors during the war.     Entre 2004 y 2016, la guerrilla colombiana de las FARC-EP pasó por varias mutaciones antes de firmar un acuerdo de paz que marcó el fin de su lucha armada. En cada una de estas etapas, lo que los guerrilleros llamaban “propaganda” ha jugado un papel central en la estrategia del grupo. Este artículo analiza 37 números de Resistencia, la revista publicada clandestinamente por las FARC-EP. Interroga críticamente la evolución de la representación de la mujer combatiente, elemento central del discurso fariano y de la guerra propagandística en Colombia. Revela dos estrategias sucesivas. En un primer tiempo, las FARC-EP desarrollaron un discurso de compensación simbólica, ofreciendo a las mujeres farianas constantes homenajes en su revista, pero dejando poco espacio para la expresión de la voz femenina. A partir de 2012, se observa una progresiva transversalización del género, que corresponde a la emergencia de figuras femeninas de primer plano tanto en la mesa de negociación como en las páginas de Resistencia. Confirmando los efectos materiales que puede tener el discurso feminista sobre las organizaciones insurgentes, el análisis también revela la persistencia en Colombia de estrategias discursivas que buscan reciclar estereotipos de género militarizados producidos por los actores armados durante la guerra. 

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

International audienceWe address the simulation of dynamic crack propagation in brittle materials using a regularized phase-field description, which can also be interpreted as a damage-gradient model. Benefiting from a variational framework, the dynamic evolution of the mechanical fields are obtained as a succession of energy minimizations. We investigate the capacity of such a simple model to reproduce specific experimental features of dynamic in-plane fracture. These include the crack branching phenomenon as well as the existence of a limiting crack velocity below the Rayleigh wave speed for mode I propagation. Numerical results show that, when a crack accelerates , the damaged band tends to widen in a direction perpendicular to the propagation direction, before forming two distinct macroscopic branches. This transition from a single crack propagation to a branched configuration is described by a well-defined master-curve of the apparent fracture energy Γ as an increasing function of the crack velocity. This Γ(v) relationship can be associated, from a macroscopic point of view, with the well-known velocity-toughening mechanism. These results also support the existence of a critical value of the energy release rate associated with branching: a critical value of approximately 2Gc is observed i.e. the fracture energy contribution of two crack tips. Finally, our work demonstrates the efficiency of the phase-field approach to simulate crack propagation dynamics interacting with heterogeneities, revealing the complex interplay between heterogeneity patterns and branching mechanisms

Simulation de fissures courbes en trois dimensions avec extraction directe des facteurs d'intensité des contraintes : En vue de l'identification de lois de propagation de fatigue

It is necessary to understand the behavior of structures up to their failure to enhance their design. The mechanisms and phenomena undergoing failure vary according to the considered material and boundary conditions. We consider homogeneous materials for which cracks propagate in a context where behavior nonlinearities are not dominants. These conditions are matched for brittle and quasi-brittle materials and for some fatigue cracks. For the former, the main source of dissipation is the crack propagation which can be seen as the generation of a new free-surface. For the later, there is many applications where, in one loading cycle, the nonlinearities remains confined around the crack tip. The linear elastic fracture mechanics theory is then a pertinent model to approximate the structure behavior. Under such hypotheses, a singularity appears in the crack tip vicinity. The Williams' series expansion is computed from the asymptotic study of plane and anti-plane states. The stress is singular at the crack tip and the order of this singularity is one out of two. The singularity amplitude is quantified by the stress intensity factors (SIF), one for each of the three loading modes. In 3D, the crack shape is potentially complex (front curvature and non-planar crack), and no general asymptotic series expansion exists. In this PhD thesis, the 2D Williams' series in displacements are used and regularized with a finite element evolution along the front. From this 3D definition of the asymptotic fields in the crack tip vicinity, a numerical method for direct estimation of the SIF (DEK-FEM) is extended to 3D. This method is based on domain decomposition, the two domains are bounded in a weak sense on their interface. In the crack tip vicinity, the mechanical fields are approximated by a truncation of the asymptotic series expansion. Therefore, appropriate fields are used to deal with the singularity, and the associated degrees of freedom are directly the asymptotic coefficients. Among these coefficients are the SIF and the T-stresses. To bridge the scales between the structure and the crack front singularity and to increase the numerical efficiency, this method is embedded in a localized X-FEM multigrids approach. The proposed method is shown to provide an accurate evaluation of the SIF and T-stresses evolution. This approach has been developed in combination of an experimental post-processing method (full field displacement measurement through image correlation) based on the same asymptotic series expansion. The 3D images can be obtained for in situ fatigue experiments by X-ray microtomography and reconstruction. The crack geometry and the SIF are then provided by image correlation and regularization based on Williams series expansion. These data can be used for identifying a 3D fatigue crack growth law. The efficiency of the method is illustrated in 2D.La compréhension du comportement de structures jusqu'à leur ruine est nécessaire pour concevoir au mieux ces structures. Selon le matériau et les sollicitations considérées, les mécanismes physiques à l'origine de la rupture changent. Nous nous intéresserons à des matériaux homogènes pour lesquels la ruine passe par le développement de fissures autour desquelles les non-linéarités de comportement n'ont pas un rôle dominant. Ces conditions sont réunies pour les matériaux fragiles pour lesquels la source principale de dissipation est la génération non réversible d'une surface libre, et pour certaines fissures de fatigue. Sur un cycle de chargement, il existe de nombreuses applications pour lesquelles les non-linéarités restent confinées. La théorie de la mécanique linéaire élastique de la rupture est alors un modèle pertinent pour approcher le comportement de la structure. Sous ces hypothèses, le front de la fissure introduit une singularité. L'étude asymptotique de cette singularité dans des situations plane et anti-plane permet de définir les séries de Williams. La singularité est alors d'ordre un demi et elle est quantifiée par les facteurs d'intensité des contraintes (FIC) pour chacun des trois modes de sollicitations. En 3D, la fissure peut avoir une géométrie complexe, et aucune expression générale de la singularité n'existe. Dans cette thèse, les séries de Williams en déplacements sont utilisées et régularisées le long du front au sens des éléments finis. À partir de cette définition 3D des séries asymptotiques en pointe de fissure, une méthode d'extraction directe des FIC (DEK-FEM) est étendue au cas 3D. Le domaine est décomposé en deux domaines, raccordés en moyenne sur l'interface. Au voisinage du front, les champs mécaniques sont approchés par une troncature des champs asymptotiques. La singularité est donc traitée avec des champs adaptés, et les degrés de liberté associés sont directement les coefficients asymptotiques. Parmi ces coefficients asymptotiques, on retrouve les FIC et les T-stresses. Pour des raisons d'efficacité numérique et pour pouvoir relier l'échelle de la structure à l'échelle de la fissure, cette méthode est intégrée dans un contexte multigrilles localisées X-FEM. Ainsi nous montrons que cette approche permet une bonne évaluation des évolutions des FIC et du T-stress. Cette méthode est développée en parallèle d'une stratégie de post-traitement expérimental (mesure de champs de déplacements par corrélation d'images) basée sur les mêmes séries asymptotiques. Les images tridimensionnels d'un essai de fatigue in situ sont obtenues par micro-tomographie à rayons X et reconstruction. La corrélation et la régularisation basées sur les séries asymptotiques permettent d'obtenir la géométrie de la fissure et les FIC pour pouvoir identifier des lois de propagation de fissures 3D en fatigue. L'efficacité de cette méthode en parallèle d'une simulation DEK-FEM est illustrée en 2D

Fast 4D tensile test monitored via X-CT: Single projection based Digital Volume Correlation dedicated to slender samples

International audienceThe measurement of 4D (i.e., 3D space and time) displacement fields of in situ tests within X-ray Computed Tomography scanners (i.e., lab-scale X-CT) is considered herein using projection-based Digital Volume Correlation. With one single projection per loading (i.e. time) step, the developed method allows for loading not to be interrupted and to vary continuously during the scan rotation. As a result, huge gains in acquisition time (i.e., more than two orders of magnitudes) to be reached. The kinematic analysis is carried out using predefined space and time bases combined with model reduction techniques (i.e., Proper Generalized Decomposition with space-time decomposition). The accuracy of the measured kinematic basis is assessed via gray level residual fields. An application to an in situ tensile test composed of 127 time steps is performed. Because of the slender geometry of the sample, a specific beam space regularization is used, which is composed of a stack of rigid sections. Large improvements on the residual, whose SNR evolves from 9.9 dB to 26.7 dB, validate the procedure

Sub-minute in situ Fracture Test in a Lab CT-scanner

International audienceThe present study aims at demonstrating the feasibility of performing a fracture test in less than one minute in a lab CT scanner despite the severe time constraints of tomography acquisition. After introducing the basic concepts of Projection-based Digital Volume Correlation (P-DVC), the specific implementation of this methodology to a wedge splitting test on a refractory material is presented. The kinematics of the test is described over a mesh tailored to the sample geometry, and the elastic behavior of the sample is exploited through finite element computations to provide sensitivity fields of experimental boundary conditions to allow for their "measurements." Enhancing the simulation to account for crack advance with extended finite element analyses allows the sensitivity of the procedure to the crack position to be assessed. A confidence interval for the refractory toughness is finally obtained

Spin-motion coupling in a circular Rydberg state quantum simulator: case of two atoms

Rydberg atoms are remarkable tools for the quantum simulation of spin arrays. Circular Rydberg atoms open the way to simulations over very long time scales, using a combination of laser trapping of the atoms and spontaneous-emission inhibition, as shown in the proposal of a XXZ spin-array simulator based on chains of trapped circular atoms [T.L. Nguyen $\textit{et al.}$, Phys. Rev. X 8, 011032 (2018)]. Such simulators could reach regimes (thermalization, glassy dynamics) that are out of the reach of those based on ordinary, low-angular-momentum short-lived Rydberg atoms. Over the promised long time scales, the unavoidable coupling of the spin dynamics with the atomic motion in the traps may play an important role. We study here the interplay between the spin exchange and motional dynamics in the simple case of two interacting circular Rydberg atoms confined in harmonic traps. The time evolution is solved exactly when the position dependence of the dipole-dipole interaction terms can be linearized over the extension of the atomic motion. We present numerical simulations in more complex cases, using the realistic parameters of the simulator proposal. We discuss three applications. First, we show that realistic experimental parameters lead to a regime in which atomic and spin dynamics become fully entangled, generating interesting non-classical motional states. We also show that, in other parameter regions, the spin dynamics notably depends on the initial temperature of the atoms in the trap, providing a sensitive motional thermometry method. Last, and most importantly, we discuss the range of parameters in which the motion has negligible influence over the spin dynamics.Comment: 18 pages, 12 figure

Towards quantum simulation with circular Rydberg atoms

The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation

Variational phase field model for dynamic brittle fracture

Simulating crack nucleation and propagation remains a challenging problematic because of the complexity of crack patterns observed in fracture mechanics experiments. Whereas some numerical methods aim at explicitly tracking the crack front evolution, an interesting alternative is offered by continuous approaches of brittle fracture which consist in representing the crack topology using a continuous field varying from 0 (sound material) to 1 (fully cracked material) across an internal length scale. This « phase field » approach benefits from a variational framework, strongly related to gradient damage models, and can be seen as a regularization of the variational approach to fracture developed by Francfort and Marigo in 1998. Moreover, it does not require any a priori knowledge of the crack path or topology, its evolution being driven only by energy minimization. Using such an approach combined to a finite-element discretization, the present work aims at providing some insights on crack propagation in a dynamic context. More specifically, crack branching (splitting of a single crack in two or more cracks) is a characteristic phenomenon of dynamic brittle fracture which still lacks a sound theoretical explanation. Numerical simulations will help us better understand some aspects of the branching phenomenon, especially the role played by material heterogeneities in the onset or delay of crack branching